Quod Erat Demonstrandum

2009/05/30

WolframAlpha

Filed under: Information — johnmayhk @ 10:32 下午
Tags:

Gower 介紹了 WolframAlpha,值得推介:

http://www94.wolframalpha.com

比如要找 3^100 的頭十個位,又或是在 1000 至 2000 內的所有質數,全不費力。我略略在其網頁輸入:

the first 10 digits of 3^100
prime numbers between 1000 and 2000
euler constant
napier number
100 digits of e
200 digits of pi

立即得出解答,數學人應該用得著。

2009/05/23

點數差的期望值

Filed under: Additional / Applied Mathematics,HKALE,HKCEE,mathematics — johnmayhk @ 3:03 下午

擲兩顆公平骰子一次,求兩個點數差的期望值。

學生甲:

嗯,擲一顆骰子,點數的期望是 \frac{1}{6}(1+2+3+4+5+6) = 3.5。無論擲兩顆,三顆,它們的點數期望值皆是 3.5,故此,兩個點數差的期望值就是 3.5- 3.5= 0(more…)

2009/05/15

幾何舞術

Filed under: Fun — johnmayhk @ 11:18 下午

20090514-geometry-dance-1

20090514-geometry-dance-2

Source: metropop 154

未想過可以如此 crossover,這三樣都喜愛,但時間不許我做太多「無謂野」…

Details: (看看當中的 video)
http://www.frenchmay.com/posts/program_detail/91

2009/05/13

數數唸

一.

以下數字是「旋轉對稱」的嗎?

1961 (more…)

2009/05/12

用 logarithm 計出頭幾個位

Filed under: HKCEE,mathematics — johnmayhk @ 12:05 下午
Tags: ,

昨天匆匆出了份中四 logarithm 的習作,其中一題:

Find the first digit of 1997^{2009}.

留意,我們不是找「個位」,而是找「第一個位」是什麼。 (more…)

2009/05/11

[FW][News] 豆腐渣奪去完美女兒 「等待真相」

Filed under: Life,Report — johnmayhk @ 3:23 下午

(明報)2009年5月10日 星期日 05:05

【明報專訊】Angel一直沒有忘記劉小英與富新母親們,劉小英則一直念念不忘亡女畢月星,「她在我心中是最完美的,豆腐渣把她奪去了,我每天晚上都夢見她回來,我們還欠一個公道!」 (more…)

2009/05/10

[FW] 向社會推薦優良數學科普書籍

Filed under: Fun,mathematics — johnmayhk @ 2:41 下午

http://www.math.sinica.edu.tw/mrpc_jsp/book/about.jsp

同學,有時間看看短短的書介,找有興趣的題目深入研究研究吧!

2009/05/07

快打一篇

Filed under: Life,mathematics — johnmayhk @ 9:27 下午

很累,唯有寫字減壓。

今天中四的同學 KM 問, 是有理數還是無理數,我真是答不出來 (more…)

2009/05/06

2009 CE Additional Mathematics Paper Section B

Filed under: Additional / Applied Mathematics,HKCEE — johnmayhk @ 6:04 下午

重點題目:

以下是 2009 CE Additional Mathematics Q.18,同學,看看你可否在 16 分鐘內正確地完成它:

The following figure shows a park AED on a horizontal ground. The park is in the form of a right-angled triangle surrounded by a walking path with negligible width. Henry walks along the path at a constant speed. He starts from point A at 7:00 am. He reaches points B, C and D at 7:10 am, 7:15 am and 7:30 am respectively and returns to A via point E. The angles of elevation of H, the top of a tower outside the park, from A and D are 45^o and 30^o respectively. At point B, Henry is closest to the point K which is the projection of H on the ground. Let HK = h m.

(a) Express DK in terms of h. (1 mark)
(b) Show that AB = h\sqrt{\frac{2}{3}} m. (3 marks)
(c) Find the angle of elevation of H from C correct to the nearest degree. (3 marks)
(d) Henry returns to A at 8:10 am. It is known that the area of the park is 9450 m^2.
(i) Find h.
(ii) A vertical pole of length 3 cm is located such that it is equidistant from A, D and E. Find the angle of elevation of H from the top of the pole correct to the nearest degree. (5 marks) (more…)

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